Algebra-2

To determine the equation of the exponential function that fits the given table, we can analyze the points provided. The key points on the table are:

(0, 20)

(1, 60)

(2, 180)

(3, 540)

 

The general form of an exponential function is , where a is the initial value and b is the base.

 

Notice the relationship between consecutive y-values:

From (0, 20) to (1, 60), y goes from 20 to 60.

From (1, 60) to (2, 180), y goes from 60 to 180.

From (2, 180) to (3, 540), y goes from 180 to 540.

 

This consistent multiplication by 3 suggests that b=3.

 

Since (0, 20) is on the graph, substituting x = 0, y = 20 and b = 3 into the equation gives:

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